The only cheap holiday we've been on was one off Teletext in Crete a few years back at £150 each for a week.
It was allocation on arrival, so you're really at the mercy of the holiday company for what the accomodation is like. We got lucky and got a small block of appartments about 200 yards from a decent beach.
It was in a really OTT tourist trap area, though - so we stayed away from the nightlife, which was all theme pubs and stuff - again, luckily, the accomodation was well off the main strip, and there was only one group of youngsters there, who were well behaved anyway, so it was pretty quiet too - a really good holiday all in.
That said, I think we got REALLY lucky with that one, and although I'd be willing to try it again if it was just for a £150 punt, I don't think I'd gamble like that with a precious weeks' holiday again - if the next one was rubbish, I wouldn't really begrudge the cash, but I'd be gutted about "wasting" a week of leave.
If we were looking to get a cheap Med holiday again, I'd instead try to find a group of 4-6 friends (probably other couples with young kids like us) and group-rent an out-of-town villa with a couple of cars instead. You can get the individual price for a self-catering villa in Majorca or something pretty damn low too, with a much lower risk of loud/rubbish accomodation.